Find the solutions of the equation by completing the square.
x^2-6x=7_
x^2-6x_= 7_
(x-_)^2 =_
x-3=_
x-3=_ and x-3 =_
What is the smallest value of x
What is the largest value of x
To complete the square for x^2 - 6x = 7, we need to add (6/2)^2 = 9 to both sides of the equation:
x^2 - 6x + 9 = 7 + 9
(x - 3)^2 = 16
Now we take the square root of both sides:
x - 3 = ±√16
x - 3 = ±4
There are 2 solutions:
x - 3 = 4 --> x = 7
x - 3 = -4 --> x = -1
Therefore, the smallest value of x is -1 and the largest value of x is 7.